Lesson 1E: Vapor Pressure and Viscosity

Key Definitions

• Vapor Pressure: The pressure exerted by vapor molecules when in phase equilibrium with its liquid molecules at a given temperature.
  • Saturation Pressure (P_sat): Equivalent term used in thermodynamics.
• Cavitation: Occurs when pressure in a liquid drops below the vapor pressure, causing the liquid to vaporize into bubbles.
• Viscosity (μ): Represents the internal resistance of a fluid to motion. Also known as dynamic viscosity.

Vapor Pressure

• Equilibrium: Occurs when the amount of molecules evaporating equals those returning to the liquid.
• Units: Typically measured in Pascals (Pa) or kilopascals (kPa).
• Cavitation Example: Water at 20°C with a flow pressure of 3.220 kPa does not cavitate because the pressure is greater than vapor pressure (2.339 kPa).

Cavitation

• Effects: Causes noise, vibrations, and potential damage to surfaces such as ship propellers and pipes.
• Phenomenon: Bubbles collapse rapidly in higher pressure regions leading to "cavitation damage."

Viscosity

• Symbol: μ, sometimes represented as η.
• Units: kg/m·s (kilograms per meter second) or poise (P), centipoise (cP).
• Kinematic Viscosity (ν): Defined as μ divided by density, with units m²/s (meters squared per second).
• Temperature Dependence:
  • Gas viscosity increases with temperature.
  • Liquid viscosity decreases with temperature.

Viscosity in Practice

• Sutherland's Law: Used for calculating the viscosity of gases as a function of temperature.
  • Example Calculation: Viscosity of air at 50°C = 1.9661 x 10^-5 kg/m·s.
• Empirical Equations: Available but not discussed in detail.

Newtonian vs Non-Newtonian Fluids

• Newtonian Fluids: Rate of deformation is linearly proportional to shear stress.
  • Examples: Water, air, oils.
• Non-Newtonian Fluids: Non-linear relationship between shear stress and deformation rate. Types include:
  • Dilatant (Shear-Thickening): e.g., starch in water.
  • Pseudoplastic (Shear-Thinning): e.g., paint, blood.
  • Bingham Plastic: Requires a yield stress before flowing, e.g., toothpaste.

Example Problems

• Block on Incline: Calculating the speed of a block sliding down an incline covered with an oil film.
  • Viscous force and speed calculations using Newton's second law.

Applications

• Journal Bearings: High viscosity oils are used to support high loads and manage heat.

These notes provide a comprehensive summary of the key points from the lecture on vapor pressure and viscosity, including definitions, practical examples, and applications.